What are the various techniques for clearing floats?

Floats are still incredibly common. As this is published, still probably the most cross-browser consistent way to build layout and grids. Anyone who has worked with them is aware of float collapsing. That is, floated element do not add to the height of a parent element. So for example if a parent element contained only floated elements, it would collapse to zero height. You can deal with that like:
Use a clearfix (bonus points for micro clearfix).
Float the parent as well.
Use an overflow property other than “visible” on the parent (bonus points for listing downsides like cutting off shadows).
As a bonus question, you could ask them to compare using inline-block and floats for building a grid. Good answer: there are problems either way. With inline-block you need to deal with the whitespace issue. With floats you need to deal with clearing.